\(\text{Ta có:}\left\{{}\begin{matrix}a:15\text{ dư }2\\b:18\text{ dư }5\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}a-2⋮15\\a-5⋮18\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}a-2+15⋮15\\a-5+18⋮18\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a+13⋮15\\a+13⋮18\end{matrix}\right.\)
\(\Rightarrow a+13\in BC\left(15;18\right)\)
\(\text{Mà }\left(15;18\right)=1\)
\(\Rightarrow a+13\in B\left(90\right)\Rightarrow a+13⋮90\)
\(\Rightarrow a+13=90k\)
\(\Rightarrow a=90k-13=90k-90+90-13=90\left(k-1\right)+77\)
\(\text{Vì }\left[90k\left(k-1\right)+77\right]\text{ chia 90 dư 77}\)
\(\Rightarrow a:90\text{ dư 77}\)
